It really depends on what you want, anime isn’t so much a genre as it is a style, anything you find on American TV you can probably find something of a similar style in anime.
The following is a short list of some of my favorites and what genre it is along with a short description (I really should save this to a text file sometime), it might give you an idea what to look for.
Genre: Action / Drama
Plot: The story follows two assassins, Mireille Bouquet and Kirika (I forget her last name) as they try to uncover the secret of their past that links them both and leaving a path of death and destruction in their wake. Very violent, but almost no blood, there’s no gore what so ever, but you’ve got people getting killed constantly, some of them innocent. Its very good, but not for the faint of heart.
Note: Its currently being released on DVD
Seikai no Senki (Banner of the Stars)
Genre: SF (Science Fiction) / Action
Plot: The sequel to Crest of the Stars, it picks up 2 years where Crest of the Stars left off. After several major battles between the Abb and the rest of humanity both sides have lost most of their fleet so a temporary peace is established while all sides rebuild, but soon the Abb launch a new offensive in an attempt to break through the enemy’s defenses and rejoin with their colonies beyond enemy space. The story follows Lafiel and Jinto as they command a small frigate as part of the Abb fleet. It’s a fantastic series with great space battles, there’s a single fight that lasts from episode 8 to episode 12, and its not because of constant narration and staring at each other, there’s constant action with ships blowing up all around.
Not: DVD 1 is currently available, but very hard to find.
Mugen no Ryvius (Infinite Ryvius)
Genre: SF / Drama
Plot: In the future a strange solar event has create some kind of nebula in the Sol system, this nebula, centered on the planetary plane is a real hazard to navigation as the incredible gravitational forces in its depths can crush any ship. The story revolves around a group of students training at the navigational academy, during an attack by unknown forces the station is damaged and begins to sink into the nebula; the students are forced to flee onto a strange cruiser hidden at the station. The students escape on the mysteries ship, but all the instructors are killed in the attack, however things go from bad to worst as they soon discover that the entire earth navy is out to destroy them and they don’t even know why. Its an excellent, but very dark series, very reminiscent of the “Lord of the Flies,” it doesn’t take long before order breaks down and the students start turning on each other.
Not: Not available on DVD, but its not too hard to find if you ask around anime channels.
Arc the Lad
Genre: Action / Fantasy
Plot: Based on the video game bearing the same title and produced by Hideo Katsumata, Arc the Lad is the tale about Elk, a young bounty hunter, who has been blessed by the Spirit of Fire. Responding to a distress call on board a hijacked air ship, Elk rescues a mysterious girl, Lieza, and her wolf companion Pandit. The three uncover a series of government conspiracies where grotesque, chimera experiments are conducted on children with the powers of the Sacred Spirits, of which Elk had escaped from. In the middle of it all is Arc, whom Elk believes is responsible for the destruction of his village and parents.
Note: The summary was original written by Animesou; I think you can find it on DVD
Genre: SF / Action
Plot: The story follows an unlikely group of bounty hunters as they travel around the Sol system trying to make a few bucks to make things worst their past keeps coming back to haunt them. The series has some great music by Yoko Kano as well as some very touching episodes, Bebop is a strange series, you can find a lot of thinks in here that you might not expect, I suggest you take a look.
Note: Available on DVD
Genre: Action / Comedy / Drama
Plot: Some time in the future humans have colonized a desert planet, the story takes place there. The plot follows an odd character called Vash the Stampede, the so called humanoid typhoon, a man who leaves a trail of destruction where ever he goes, its not that he’s evil, just that cities tend to get destroyed when he’s around. Trigun is a strange series, it starts off light and funny, but it gets really dark, really fast. I don’t want to spoil anything, but the first 13 episodes are nothing like the rest of the series and by the end no one’s laughing anymore.
Note: Available on DVD.
Genre: Wacky Experimental Anime (I’m not kidding, that’s what it is, or something close to it)
Plot: Plot? What’s that? Seriously, the plot in Excel Saga takes so many bizarre twists and turns it’s hard to follow it sometimes, but it doesn’t matter because it’s hilarious. The bare-bones of the plot is, the ideal organization Across plans to take over the world (whee, original) Il Palazzo, the leader of Across (sorta) hires Excel as an executive officer. Excel is a bubbley, air-headed and hyper girl. And she fails. A lot. The series progresses with many botched plans for city-domination, and usually in each episode they take a certain genre, and parody it. For example, episode 2 parodies Science Fiction, Episode 4 parodies romance/comedies and those dating simulation games we always get gypped out of over here, Episode 7 parodies horror, and so on. It’s all pretty random, but the anime is fall-out-of-your-chair funny.
Note: summary originally written by Spoony Bard; not available on DVD and it can be surprisingly hard to find.
Slayers, Slayers NEXT, Slayers TRY (and a few movies and OVAs):
Plot: The story revolves around Sorcery Genius Lina Inverse, a young girl with enough magical power to level a city as she tries to get rich quick and ends up saving the world from the forces of darkness all the while trying to show up her sister. I really love Slayers, it has your usual group of clichéd characters, the idiot fighter, the over enthusiastic self-righteous cleric, the depressive fighter/mage, and of course Lina, whose’s best describe as a Robin Hood who takes from the rich and keeps for herself. Add to that a mix of strange characters, weird villains and weirder allies and you’ll see why I like it so much. Its just a fun series to watch.
Note: This is the series that got me hooked on anime. Some series are available on DVD, but hard to find while some are just impossible to find even in anime channels.
There’s lots of other good, stuff, but I’m tired of typing, I’ll let some of the others do a little work.